Thermal Oxidation of General Properties of O 2 Applications of thermal O 2 Deal-Grove Model of Oxidation Thermal O 2 is amorphous. Weight Density = 2.20 gm/cm 3 Molecular Density = 2.3E22 molecules/cm 3 O2 <> Crystalline O 2 [Quartz] = 2.65 gm/cm 3
Thermal O 2 Properties () Excellent Electrical Insulator Resistivity > E20 ohm-cm Energy Gap ~ 9 ev (2) High Breakdown Electric Field > 0MV/cm (3) Stable and Reproducible /O 2 Interface (4) Conformal ide growth on exposed surface Thermal Oxidation O2 2
(5) O 2 is a good diffusion mask for common dopants D Thermal O 2 Properties cont. D sio << e.g. B, P, As, Sb. 2 si O 2 *exceptions are are Ga Ga (a (a p-type dopant) and and some metals, e.g. e.g. Cu, Cu, Au Au (6) Very good etching selectivity between and O 2. O 2 HF dip 3
Steam generation for wet idation 4
Thickness of consumed during idation original surface O 2 X si X X si = X N N si molecular density of O2 atomic density of 22 3 = X = 0. 46 X 22 3 2.3 0 5 0 molecules / cm atoms / cm 5
For -dimensional planar ide growth µm idized 2.7 µm O 2 Suggested calculation exercise: µm diameter sphere completely idized.3 µm diameter O 2 sphere O2 6
Kinetics of O 2 Growth Oxidant Flow (O 2 or H 2 O) Gas Diffusion Solid-state Diffusion O 2 Formation Gas Flow Stagnant Layer O 2 -Substrate 7
Deal-Grove Model C G stagnant layer C s O 2 Note C ss C o C o C i X 0x F F 2 F 3 gas transport flux diffusion flux through O 2 reaction flux at interface 8
F = h C C F 2 F = D 3 = ( ) G G S C x C D k C s i Mass transfer coefficient [cm/sec]. o X C i Fick s Law of Solid-state Diffusion Diffusivity [cm 2 /sec] Surface reaction rate constant [cm/sec] Comment: The derivation used in Jaeger textbook assumes F is large (not a rate-limiting factor for growth rate). Hence, the algebra looks simpler. However, the lecture notes derivation includes gas transport effect and can be directly applied to CVD growth rate which will be discussed in later weeks. 9
How to solve the idant concentrations? C S and C o are related by Henry s Law C G is a controlled process variable (proportional to the input idant gas pressure) Only C o and C i i are the 2 unknown variables which can be be solved from the steady-state condition: F = F 2 =F =F 3 (( 2 equations) 0
Derivation of Oxidation Growth Rate C = H P o s Henry s Law Henry s constant partial pressure of idant at surface [in gaseous form]. = H ( kt C ) s from ideal gas law PV= NkT C s = C o HkT
Derivation of Oxidation Growth Rate cont. Define C A F can be re-written as: h F = G HkT ( C C A o ) h ( HkT C G Using the steady-state condition: ) This is a control process variable. For a given idant pressure, C A is known. Conservation of mass flux F = = F F 2 3 2 2 equations to to solve the 2 unknowns: C o & C i i 2
Derivation of Oxidation Growth Rate cont. Therefore C i = C k + + h A kx D s s C k = + s X Ci D o F ( = F = F = F ) 2 3 = k s C i = + k k s h C k + s A s X D 3
Now, convert F into Oxide Thickness Growth Rate F = N dx dt X Oxidant molecules/unit volume required to form a unit volume of O 2. O 2 F { t} Therefore, we have the ide growth rate eqn: N dx dt = + k k s h C A k + s s X D 4
Initial Condition: At t = 0, X = X i O 2 O 2 x Solution X 2 + AX = B( t +τ ) A B 2D( k 2 DC N s A + h ) Note: h >>k s for typical idation condition τ = X 2 i + AX B i 5
Note : dry and wet idation have different N factors N N 22 3 = 23. 0 / cm for O 2 as idant + O O 2 2 22 3 = 46. 0 / cm for H 2 O as idant + 2H O O + 2H 2 2 2 6
X Summary of Deal-Grove Model t X 2 X 2 t + AX dx dt 0 x + = A B ( t dx dt + τ ) = B t dx dt = A B + 2X Oxide Growth Rate slows down with with increase of of ide thickness 7
A X = + 2 t+ τ A 2 4 B (Case ) Large t [ large X ] X Bt (Case 2) Small t [ Small X ] X B A t 8
Deal-Grove Model Parameters () 2 D C B A N D D e Q kt Q = activation energy for diffusion (2) B A = ( h + k s ) C N A k s e ' Q kt Q = activation energy for interface reaction For thermal idation of of,, h is is typically >> >> k s s B/A is is k s s (i.e. F is is rarely the rate-limiting step) 9
B = Parabolic Constant B/A = Linear Constant 20
Oxidation Charts The The charts are are based on on X i = i 0!! 2
Two Ways to Calculate Oxide Thickness Grown by Thermal Oxidation E.g. O 2 x i= 4000A 00 o C 33min steam O 2 x o x Method : Find B & B/A from Charts Solve X 2 + AX = B( t +τ ) 22
Method 2: Use Oxidation Charts 6500 o A 4000 o A Two Ways to Calculate Oxide Thickness Grown by Thermal Oxidation X 00 o C T 3 T 2 T The The charts are are based on on X i =0 i =0!! X i 0 24 33 5 7 = 4000 A τ = 24 min Total effective idation time ( 24 33) min = 57min time(min) at 00 o C from chart + if start with = 0 X i 23
() Grown at 000 o C, 5hrs (3) CVD Oxide O 2 4000 o A x i O 2 4000 o A CVD Oxide (2) Grown at 00 o C, 24min O 2 4000 o A For same X i, i τ is the same for all three cases shown here 24